My late husband had two adult kids at the point when he found out about his ex's affair.
He and his ex divorced two years later. We married 6 yrs after that. Yet another 6 yrs later, one of the kids became a mother.
She told us that I was "too young" to be a grandmother. (Fair enough. The age difference between my husband and me was almost the same as that between her and her partner - he had two adult children when they got together - so maybe that's what was in her mind. )
My husband's suggestion of "honorary aunty" was knocked back. I reckoned that it was up to the mum to decide, so was always called by forename.
Cut to around 7 years later. The ex's Affair Partner died. The daughter's partner had a few drinks while they were visiting and announced that he was displeased that the AP had left all his money to the ex. "He should have left something to [granddaughter] because she called him 'Grandad'."
That was the point when I thought "Oh. You'll obviously not expect me to leave the bairn anything then?"
When the granddaughter was about 11, in front of her mother she asked me what relation I was to her. I was taken aback - she's an intelligent enough girl, and I couldn't understand how she didn't have it figured out.I explained that I was married to her grandfather, so her step-grandmother. "Is that like half a gran?"
"Well, I suppose you could put it that way." All the while, the mother was laughing.
DH died during lockdown. The daughter told me that she couldn't come to the funeral because of her asthma. She didn't want the nearly 21 yr old granddaughter to attend because it might be too upsetting.
I was executor. The granddaughter wasn't in his will, but he'd told me what to give her on his behalf. I honoured that. I also had my MIL's jewellery repaired and sent that to her. When she graduated, I sent her another cheque from my husband's estate. (My DH hadn't told me to do that, but I knew that he'd have given her something.)
I suspect that they all expected more. I don't think they realised that I was the main breadwinner. My husband's combined teaching and state pension was 18k a year. I had to give up my job two years sooner than expected because of my husband's health and my pension has taken a severe knock as a result.
The granddaughter will get nothing from me. If there's anything left when I go, it'll go to the children who call me "Great Aunt". I feel a bit sad about it.
ETA The point I'm making is that I understand the OP's logic.